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The cosparse analysis model has been introduced recently as an interestingalternative to the standard sparse synthesis approach. A prominent questionbrought up by this new construction is the analysis pursuit problem -- the needto find a signal belonging to this model, given a set of corrupted measurementsof it. Several pursuit methods have already been proposed based on $\ell_1$relaxation and a greedy approach. In this work we pursue this question further,and propose a new family of pursuit algorithms for the cosparse analysis model,mimicking the greedy-like methods -- compressive sampling matching pursuit(CoSaMP), subspace pursuit (SP), iterative hard thresholding (IHT) and hardthresholding pursuit (HTP). Assuming the availability of a near optimalprojection scheme that finds the nearest cosparse subspace to any vector, weprovide performance guarantees for these algorithms. Our theoretical studyrelies on a restricted isometry property adapted to the context of the cosparseanalysis model. We explore empirically the performance of these algorithms byadopting a plain thresholding projection, demonstrating their good performance.

Greedy-Like Algorithms for the Cosparse Analysis Model